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GPU-Accelerated Optimization-Based Collision Avoidance

Zeming Wu, Zhuping Wang, Hao Zhang

TL;DR

A novel collision avoidance constraint is proposed based on scale-based collision detection and the strong duality of convex optimization, which can be decomposed into several low-dimensional quadratic programmings (QPs) following the paradigm of alternating direction method of multipliers (ADMM).

Abstract

This paper proposes a GPU-accelerated optimization framework for collision avoidance problems where the controlled objects and the obstacles can be modeled as the finite union of convex polyhedra. A novel collision avoidance constraint is proposed based on scale-based collision detection and the strong duality of convex optimization. Under this constraint, the high-dimensional non-convex optimization problems of collision avoidance can be decomposed into several low-dimensional quadratic programmings (QPs) following the paradigm of alternating direction method of multipliers (ADMM). Furthermore, these low-dimensional QPs can be solved parallel with GPUs, significantly reducing computational time. High-fidelity simulations are conducted to validate the proposed method's effectiveness and practicality.

GPU-Accelerated Optimization-Based Collision Avoidance

TL;DR

A novel collision avoidance constraint is proposed based on scale-based collision detection and the strong duality of convex optimization, which can be decomposed into several low-dimensional quadratic programmings (QPs) following the paradigm of alternating direction method of multipliers (ADMM).

Abstract

This paper proposes a GPU-accelerated optimization framework for collision avoidance problems where the controlled objects and the obstacles can be modeled as the finite union of convex polyhedra. A novel collision avoidance constraint is proposed based on scale-based collision detection and the strong duality of convex optimization. Under this constraint, the high-dimensional non-convex optimization problems of collision avoidance can be decomposed into several low-dimensional quadratic programmings (QPs) following the paradigm of alternating direction method of multipliers (ADMM). Furthermore, these low-dimensional QPs can be solved parallel with GPUs, significantly reducing computational time. High-fidelity simulations are conducted to validate the proposed method's effectiveness and practicality.
Paper Structure (15 sections, 31 equations, 5 figures, 1 table)

This paper contains 15 sections, 31 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Works
  3. Collision Avoidance Constraints
  4. Collision Avoidance with Optimization
  5. Scale Based Collision Avoidance Constraints of Polyhedra
  6. Scale-based Collision Detection of Polyhedra
  7. Reformulation of Collision Constraints
  8. Collision Avoidance Based on Model Predictive Control
  9. Optimization Problem Formulation
  10. Problem Separation via ADMM
  11. Solving Multiple QPs with GPU in Parallel
  12. Computational Complexity
  13. Simulation and Benchmark Comparisons
  14. High-Fidelity Simulation
  15. Conclusion

Figures (5)

  • Figure 1: An illustration of scale-based collision detection.
  • Figure 2: The geometry of quadrotor and obstacles.
  • Figure 3: The overview of our optimization process.
  • Figure 4: One case in the simulation. (A) The environment in AirSim. (B) The geometry of obstacles, the geometry of the quadrotor, the reference trajectory and the actual trajectory during the navigation with OBCA. (C) The navigation with RDA. (D) The navigation with the proposed method.
  • Figure 5: Comparisons of computation time.